You get the Hawk right after the mission where you use it, but after that, there's a long pause of no unlocks (except for kill rate related stuff) until Heartbreak One when you get the MiG 1.44. The only missions, if I recall correctly, where you absolutely must use a naval aircraft are Ancient Walls and Sea of Chaos, and after SoC you can choose any planes, which will be the ones you fly until the end of the game.

EDIT: Gah, ninja'd, by eleven minutes. The shame!